title: A reduced computational and geometrical framework for inverse problems in hemodynamics.
abstract: The solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper, we apply a domain parametrization technique to reduce both the geometrical and computational complexities of the forward problem and replace the finite element solution of the incompressible Navier-Stokes equations by a computationally less-expensive reduced-basis approximation. This greatly reduces the cost of simulating the forward problem. We then consider the solution of inverse problems both in the deterministic sense, by solving a least-squares problem, and in the statistical sense, by using a Bayesian framework for quantifying uncertainty. Two inverse problems arising in hemodynamics modeling are considered: (i) a simplified fluid-structure interaction model problem in a portion of a stenosed artery for quantifying the risk of atherosclerosis by identifying the material parameters of the arterial wall on the basis of pressure measurements; (ii) a simplified femoral bypass graft model for robust shape design under uncertain residual flow in the main arterial branch identified from pressure measurements.
authors.affiliation: Modelling and Scientific Computing (CMCS), Mathematics Institute of Computational Science and Engineering (MATHICSE), Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 8, CH-1015 Lausanne, Switzerland.
authors.forename: Toni
authors.initials: T
authors.lastname: Lassila
authors.forename: Andrea
authors.initials: A
authors.lastname: Manzoni
authors.forename: Alfio
authors.initials: A
authors.lastname: Quarteroni
authors.forename: Gianluigi
authors.initials: G
authors.lastname: Rozza
mesh_terms: D000465:Algorithms; D050197:Atherosclerosis / Q000503:physiopathology; D001499:Bayes Theorem; D001794:Blood Pressure / Q000502:physiology; D001807:Blood Vessel Prosthesis; D003198:Computer Simulation; D003251:Constriction, Pathologic / Q000503:physiopathology; D055119:Elastic Modulus / Q000502:physiology; D005263:Femoral Artery / Q000502:physiology; D006439:Hemodynamics / Q000502:physiology*; D006801:Humans; D016018:Least-Squares Analysis; D008955:Models, Cardiovascular; D058017:Vascular Grafting
keywords: fluid-structure interaction; hemodynamics; inverse problems; model reduction; parametrized Navier-Stokes equations; reduced-basis methods; shape optimization